Sampling scopes, or equivalent time, scopes are used for acquisition of repetitive high frequency signals. The advantages of sampling scopes, as compared to real-time digitizers, are based on the fact that signal samples are taken at a relatively low sampling rate and the signal is acquired during multiple signal repetitions, so that each signal sample is taken with a varied delay relative to a trigger signal. This “equivalent time” sampling method allows high dynamic range and bandwidth which are essential for high frequency measurements (e.g., for use in optical and communications applications). For example, modern sampling scopes offer 16-bit sampling analog-to-digital (ADC) resolution with up to 80 GHz bandwidth.
Time base sub-systems of sampling scopes determine a delay τk for a current signal sample sk(t) relative to a trigger signal. Different methods for time base generation are described in the prior art, see e.g. U.S. Pat. Nos. 5,397,981, 4,812,769 and 6,564,160. So-called “Precision Time Base” modules (e.g. Keysight model 86107A and others) are factory calibrated to provide high accuracy timing of samples. However, in most practical applications, time base accuracy obtained may be insufficient for needed precision measurements due to device changes after initial factory calibration, variations of ambient temperature and other factors.
The problem of time base accuracy has attracted considerable attention in prior art publications. For example, the paper “Least-Squares Estimation of Time Base Distortion of Sampling Oscilloscopes” by C. M. Wang, P. Hale and K. Coakley (IEEE Transactions on Instrumentation and Measurements, vol. 48, 6, 1999) and “Compensation of Random and Systematic Timing Errors in Sampling Oscilloscopes”—IEEE Transactions on Instrumentation and Measurements, vol. 55, 6, 2006 by P. Hale, C. Wang and others, describe methods for correction of time base errors based on multiple sine wave signals with different frequencies and phases, or using single frequency quadrature sine waves sampled simultaneously with a signal of interest. The latter method, developed by The National Institute of Standards and Technology (NIST), is used for “Electro-Optical Sampling” calibration of high frequency sampling scopes as described in “Calibration Technique For Calibrating High Speed Equivalent Time Sampling Scope Using A Characterized High Speed Photo Diode”, B. Schriver, publication date unknown, web-published by Keysite Technologies Inc., Santa Rosa Calif., and “Correcting Sampling Oscilloscope Time Base Errors With A Passively Mode-Locked Laser Phase Locked to a Microwave Oscillator”, J. Jargon, P. Hale and C. Wang, IEEE Transactions on Instrumentation and Measurement, vol. 59, 2010. However, the described methods have a number of disadvantages. They require a generation of high frequency quadrature signals, which is complicated. At least three sampling scope channels (two for calibration signals and one for an analyzed signal) are required for a calibration procedure. Moreover, time base calibration using laser diodes requires a sophisticated electro-optical setup and generally can only be done in a dedicated facility. Also, these calibration methods are based on a complicated numerical orthogonal distance regression method, which may not produce satisfactory results in all cases as indicated in the above-cited references.
A number of prior-art publications, such as “An Identification Technique For Data Acquisition Characterization In The Presence Of Non-Linear Distortions And Time Base Distortions” G. Vandersteen, Y. Rolain and J. Schoukens (IEEE Transations on Instrumentation and Measurement, vol. 50, 2001), “Measuring Time Base Distortions in Analog-Memory sampling Digitizers”, F. Attivissiom et al (IEEE Transactions on Instrumentation and Measurements, vol. 57, 2008) describe different methods for time base error estimations based on multiple measurements using sine wave signals with different phases or multiple reference frequencies. Time base error is calculated from multiple sets of data using a maximum-likelihood estimator based on an iterative numerical procedure which may be affected by convergence and numerical instability problems.
It is, therefore, desirable to develop a simple and practical time base correction method which does not require a complicated hardware setup, multiple input signals and frequencies, multiple auxiliary sampling scope channels and complicated numerical algorithms having potential convergence and stability issues.